1. Field of the Invention
This invention relates to a technique for reading a part of symbols uniformly arranged on a two-dimensional plane and identifying a location thereof.
2. Description of the Related Art
In recent years, the techniques have been proposed for arranging the symbols uniformly, reading the symbol, and identifying the location thereof on the two-dimensional plane. For example, the symbols are uniformly arranged on a sheet of paper on which an examination is printed. By scanning the location of the answer selected by the examinee, the selected answer is transmitted to a telecommunications carrier or the like. The system that employs the aforementioned technique has been proposed (for example, as shown in FIG. 18).
An M-sequences code is often used for coding the two-dimensional plane. The M-sequences code has the characteristics of “any two partial sequences are not identical, if the partial sequences having a length of m is extracted from the M-sequences code having a length of 2m−1.” Several techniques employing the aforementioned characteristics have been proposed for encoding the plane.
The M-sequences code denotes the code having a longest cycle (2p−1) from among the sequences created with the following expression of a p-th degree recurrence equation (also known as pseudo-random sequences).at=c1at-1+c2at-2+ . . . +cpat-p(mod 2)  (Expression 1)
For example, if P=5, C1=1, C2=1, C3=1, C4=0, and C5=1, the M-sequences (the length 25−1=31) shown in FIG. 19 is generated. As shown in FIG. 19, three partial sequences A, B, and C having the same length of p, which are taken out of difference positions in the M-sequences, are by no means identical. This characteristic enables the identification of the location on the two-dimensional coordinates with an accuracy of 1 bit.
For example, if 1 bit is represented by a symbol of 0.3 mm, the 10th degree M-sequences will be able to express the long side of a size A4 sheet having a length of 297 mm as follows.(210−1)×0.3 mm=1023×0.3 mm=306.9 mm
It is to be noted that the aforementioned expression can encode only one sheet of size A4. Encoding a huge area demands a higher M-sequences. This causes problems in that the area to be read has to be larger at the time of identifying the location on the plane, and in addition, the decoding becomes complicated.
According to Japanese Patent Application Publication No. 2003-511762 (Document 1), referring to FIG. 20, the identical M-sequences codes are arranged in parallel in a Y-axis direction on the plane to indicate the coordinate positions. The M-sequences codes arranged in parallel with the Y-axis direction are shifted from each other. For example, as shown in FIG. 20, the second line from the left is shifted by 2 bits from the third line. The third line is shifted by nine bits from the fourth line. The fourth line is shifted by 24 bits from the fifth line. The fifth line is shifted by ten bits from the sixth line. The above-mentioned M-sequences codes are the same if arranged on the same X-coordinate. In the same manner, the identical M-sequences codes are arranged in parallel in the X-axis direction on the plane to express the coordinate positions. The M-sequences codes arranged in parallel with the X-axis direction are shifted from each other. Here, a synchronization method is omitted in the description for simplification.
The technique described in Document 1, however, has to be devised for identifying an edge of the sheet of paper so as to be applied to a practically useful size such as the size A4. In other words, referring to FIG. 21, the location can be identified on an encoded whole area, yet the page identification also has to be obtained from the encoded area in order to identify the location of the page (the plane) on the encoded whole area. In addition, there is a drawback in that the redundancy in encoding becomes large by segmenting the multiple M sequences codes. Further, there is another drawback in that the calculation load becomes heavier due to the complicated algorithm for encoding and decoding.